To find the base 10 equivalent of the binary number 1011, we will break down the process step-by-step. ### Step 1: Understanding Binary Numbers Binary numbers are base 2 numbers, which means they only use two digits: 0 and 1. Each digit in a binary number represents a power of 2, starting from the rightmost digit, which represents \(2^0\). ### Step 2: Breaking Down the Binary Number The binary number 1011 can be analyzed as follows: - The rightmost digit (1) is in the \(2^0\) place. - The next digit to the left (1) is in the \(2^1\) place. - The next digit (0) is in the \(2^2\) place. - The leftmost digit (1) is in the \(2^3\) place. So, we can express the binary number 1011 in terms of powers of 2: \[ 1011_2 = 1 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \] ### Step 3: Calculating Each Term Now, we will calculate each term: - \(1 \cdot 2^3 = 1 \cdot 8 = 8\) - \(0 \cdot 2^2 = 0 \cdot 4 = 0\) - \(1 \cdot 2^1 = 1 \cdot 2 = 2\) - \(1 \cdot 2^0 = 1 \cdot 1 = 1\) ### Step 4: Summing the Values Next, we sum all these values together: \[ 8 + 0 + 2 + 1 = 11 \] ### Conclusion Thus, the base 10 equivalent of the binary number 1011 is **11**. Therefore, the correct option is **D**. ### Explanation of Other Options - **A. 8**: This option is incorrect because it only accounts for the \(2^3\) place and ignores the contributions from the other digits. - **B. 9**: This option is also incorrect. It might arise from mistakenly adding \(8\) (from \(2^3\)) and \(1\) (from \(2^0\)), but it neglects the \(2^1\) contribution. - **C. 10**: This option is incorrect as well. It could be a result of adding \(8\) (from \(2^3\)) and \(2\) (from \(2^1\)), but it fails to include the \(1\) from \(2^0\). ### Revision Summary - Binary numbers are base 2 and represent powers of 2. - Each digit in a binary number corresponds to a power of 2, starting from \(2^0\) on the right. - To convert binary to decimal, multiply each binary digit by its corresponding power of 2 and sum the results. - The binary number 1011 equals 11 in decimal (base 10).